Perturbations of spiky strings in AdS3

Abstract

Perturbations of a class of semiclassical spiky strings in three dimensional Anti-de Sitter (AdS) spacetime, are investigated using the well-known Jacobi equations for small, normal deformations of an embedded timelike surface. We show that the equation for the perturbation scalar which governs the behaviour of such small deformations, is a special case of the well-known Darboux-Treibich-Verdier (DTV) equation. The eigenvalues and eigensolutions of the DTV equation for our case are obtained by solving certain continued fractions numerically. These solutions are thereafter utilised to further demonstrate that there do exist finite perturbations of the AdS spiky strings. Our results therefore establish that the spiky string configurations in AdS 3 are indeed stable against small fluctuations. Comments on future possibilities of work are included in conclusion.

Perturbation of pulsating strings

“…The perturbation of spiky strings in flat and AdS space, in covariant formalism, has been discussed in Refs. [27,40].…”

Perturbations of giant magnons and single spikes in $\mathbb R \times S^2$

“…Given the above-stated importance of the spiky strings and giant magnons, it is worthwhile to look at the geometric properties of such string configurations from the world-sheet view point. Here following our earlier works [35], [36] we study normal deformations (linearized) about the classical giant magnon solution in R × S 2 using the well-known Jacobi equations [37][38][39][40] which govern normal deformations of an embedded surface. Earlier work in [41] dealt with computation of quantum corrections to the energy spectrum, by expanding the supersymmetric action to quadratic order in fluctuations about the classical solution.…”

“…On one hand, it helps in studying the stability properties of the string dynamics of the closed strings, and finding the quantum string corrections to the Wilson loop expectation value for the open string solutions and on the other hand, it helps us in determining the physical properties of topological defects. Apart from [35,36], related recent works on such perturbations can be found in [42][43][44][45].…”